We present a search for the production of a Higgs boson in association with a single top quark, based on data collected in 2016 by the CMS experiment at the LHC at a center-of-mass energy of
13 TeV, which corresponds to an integrated luminosity of $35.9fb^{−1}$. The production cross section for this process is highly sensitive to the absolute values of the top quark Yukawa coupling, $y_t$, the Higgs boson coupling to vector bosons, $g_{HVV}$, and, uniquely, to their relative sign. Analyses using multilepton signatures, targeting $H \rightarrow WW, H \rightarrow ττ$, and $H \rightarrow ZZ$ decay modes, and signatures with a single lepton and a $b\bar{b}$ pair, targeting the $H \rightarrow b\bar{b}$ decay, are combined with a reinterpretation of a measurement in the $H \rightarrow γγ$ channel to constrain $y_t$ . For a standard model-like value of $g_{HVV}$, the data favor positive values of $y_t$ and exclude values of $y_t$ below about $−0.9 y^{SM}_t$.